Of course, textures will look screwy for something like a body if it was not made for that body, but, other things using different textures/colors could look very cool! Have only tried on clothing/armor so far. You can even change the colors on them! Any mesh, as far as I can tell.
I just learned that in Outfit Studio, you can point a mesh to any textures in the game you like by going to properties on any separate pieces of it. Once the ball gets rolling, there will be plenty to choose from I think. It's probably not that hard to port anything yourself. I think she has had some bad experiences concerning them in the past. My favorite as well! She just doesn't want to hassle with permissions on anything.
Nearly every major texture replacer has a CBBE compatible version, for example - Fair Skin Complexion for CBBE (my current favorite skin replacer). Not use CBBE compatible textures, or not use the CBBE mod textures specifically? There are TONS of CBBE compatible textures on nexus-skyrim.